On Connection between Variationality of a Six-Order Ordinary Differential Equation and Hamilton–Ostrogradskii Equations

Abstract: In the paper, we investigate the representability of a six-orderordinary differential equation in the form ofHamilton–Ostrogradskii equations. For this purpose, potentialityconditions are obtained and the correspondingHamilton–Ostrogradskii action is constructed. © 2021, Pleiades Publishing, Ltd.